Cordero, nicknamed "Coco", throws a hard fastball—capable of reaching the upper 90s, and also has an excellent slider that he can throw for strikes early in the count, and which he uses as his outpitch.

He attended Colegio Luz Arroyo Hondo High School in the Dominican Republic.

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He was acquired after the 1999 season from the Detroit Tigers in a multi-player deal for Juan González. Cordero was the last player from that trade to play with the Texas Rangers. Coco had his most dominant year in 2004, making the AL All-Star team, but he blew some crucial saves late in September of that year to keep the Rangers from advancing to the playoffs. After blowing a team record five saves in April 2006, Cordero was removed from the closer role and replaced with Akinori Otsuka, before being traded to the Milwaukee Brewers at the trading deadline.

He was acquired on July 28, 2006 from the Rangers with Kevin Mench, Laynce Nix, and Minor Leaguer Julian Cordero (no relation) for Carlos Lee and Nelson Cruz. In 28 games with Milwaukee after the trade, he won three games, saved 16 games, and struck out 30 in 26.2 innings of work with an ERA of 1.69. His final 2006 stats were career highs of 10 wins, 84 strikeouts, 3.70 ERA, 22 saves (one of his career highs), and 75.1 innings of work between Texas and Milwaukee in 77 games (a career high). The Brewers exercised the club option on Cordero on October 6, 2006 to keep him as their closer in 2007.

On May 4, 2007 Cordero was selected as the winner of “DHL Presents the Major League Baseball Delivery Man of the Month Award” for April, 2007. This officially-sanctioned Major League Baseball (MLB) award recognizes the most outstanding relief pitcher during each month of the regular season.

In 2007 he was successful on his first 22 save attempts before, on June 9, Cordero blew his first save of the season against his former team, the Texas Rangers.